det(S - λI) = | P(x) - λI Q(x) | | -P(x) Q(x) - λI | 其中,I是单位矩阵,λ是特征值。 特征多项式的零点即为Sylvester矩阵的特征值。通过找到特征多项式的根,可以得到Sylvester矩阵的特征值。特征多项式的系数可以通过Sylvester矩阵的构造中的多项式系数来获得。 希望对你有所帮助!©...
For two polynomials P_1(x)=a_mx^m+...+a_0 and P_2=b_nx^n+...+b_0 of degrees m and n, respectively, the Sylvester matrix is an (m+n)×(m+n) matrix formed by filling the matrix beginning with the upper left corner with the coefficients of P_1(x), then shif
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MATRIX logicThis article is based on the work of Jameson who, in 1968, produced a solution of Sylvester''s matrix equation. Jameson''s method applies only to the case of a uniquesolution. In 1993 the present author produced an improved version of Jameson''s formula. Here it is proposed ...
Sylvester is a vector, matrix and geometry library for JavaScript, that runs in the browser and on the server side. It includes classes for modelling vectors and matrices in any number of dimensions, and for modelling infinite lines and planes in 3-dimensional space. It lets you write object...
The Sylvester and Frobenius Equation Problem of the Matrix s Rank; 矩阵秩的Sylvester与Frobenius等式问题5. The square matrix is called a diagonal matrix. 该方矩阵称为对角矩阵。6. The matrix is defined as the reciprocal of A. 该矩阵定义为A之逆矩阵。7...
惯性定理:指在实数域中,一个形如的二次型通过线性变换可以化简成唯一的标准型其中的正项数(称为正惯性系数)、负项数(称为负惯性系数)以及的数目唯一确定,其中的为系数矩阵的秩Sylvester惯性定理:指在实数域中,一个形如a11x12+a12x1x2+a13x1x3+⋯+annxn2的二次型通过线性变换可以化简成唯一的标准型y12+y22...
{\phantom{···}}^{m-n+1列}\\ \left[\begin{matrix} 1&&&b_0\cr &\ddots&&b_1&b_0\cr &&1&\vdots&&\ddots\cr &&&b_n&&&\ddots\cr &&&&\ddots&&&b_0\cr &&&&&\ddots&&b_1\cr &&&&&&\ddots&\vdots\cr &&&&&&&b_n \end{matrix}\right]\\ 利用Cramer法则,可得 r(x...
1) generalized Sylvester matrix 广义Sylvester矩阵 1. The relations between an R-block circulant matrix and a suitablegeneralized Sylvester matrixare presented. 讨论了两个多项式矩阵右互质时其广义Sylvester矩阵的性质,指出了广义Sylvester矩阵与R-循环分块矩阵的联系,得到了R-循环分块矩阵可逆时的充要条件。
Recently a Sylvester matrix for several polynomials has been defined, establishing the relative primeness and the greatest common divisor of polynomials. Using this matrix, we perform qualitative analysis of several polynomials regarding the inners, the bigradients, Trudi's theorem, and the connection ...